Problem: The value of $\sqrt{123}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Consider the perfect squares near $123$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $121$ is the nearest perfect square less than $123$ $144$ is the nearest perfect square more than $123$ So, we know $121 < 123 < 144$ So, $\sqrt{121} < \sqrt{123} < \sqrt{144}$ So $\sqrt{123}$ is between $11$ and $12$.